skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Type D solutions of 3D new massive gravity

Abstract

In a recent reformulation of three-dimensional new massive gravity, the field equations of the theory consist of a massive (tensorial) Klein-Gordon type equation with a curvature-squared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of new massive gravity with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity, Bianchi types II, VIII, IX, and those of non-topologically massive gravity origin, Bianchi types VI{sub 0} and VII{sub 0}. For a special relation between the cosmological and mass parameters, {lambda}=m{sup 2}, they also include conformally flat solutions, and, in particular, those being locally isometric to the previously-known Kaluza-Klein type AdS{sub 2}xS{sup 1} or dS{sub 2}xS{sup 1} solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for {lambda}=m{sup 2}. We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions.

Authors:
;  [1]
  1. Feza Guersey Institute, Cengelkoey, 34684 Istanbul (Turkey)
Publication Date:
OSTI Identifier:
21541498
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 83; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.83.084032; (c) 2011 American Institute of Physics; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; BLACK HOLES; GRAVITATION; KALUZA-KLEIN THEORY; KLEIN-GORDON EQUATION; MASS; MATHEMATICAL SOLUTIONS; METRICS; THREE-DIMENSIONAL CALCULATIONS; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD EQUATIONS; FIELD THEORIES; PARTIAL DIFFERENTIAL EQUATIONS; UNIFIED-FIELD THEORIES; WAVE EQUATIONS

Citation Formats

Ahmedov, Haji, and Aliev, Alikram N. Type D solutions of 3D new massive gravity. United States: N. p., 2011. Web. doi:10.1103/PHYSREVD.83.084032.
Ahmedov, Haji, & Aliev, Alikram N. Type D solutions of 3D new massive gravity. United States. https://doi.org/10.1103/PHYSREVD.83.084032
Ahmedov, Haji, and Aliev, Alikram N. Fri . "Type D solutions of 3D new massive gravity". United States. https://doi.org/10.1103/PHYSREVD.83.084032.
@article{osti_21541498,
title = {Type D solutions of 3D new massive gravity},
author = {Ahmedov, Haji and Aliev, Alikram N},
abstractNote = {In a recent reformulation of three-dimensional new massive gravity, the field equations of the theory consist of a massive (tensorial) Klein-Gordon type equation with a curvature-squared source term and a constraint equation. Using this framework, we present all algebraic type D solutions of new massive gravity with constant and nonconstant scalar curvatures. For constant scalar curvature, they include homogeneous anisotropic solutions which encompass both solutions originating from topologically massive gravity, Bianchi types II, VIII, IX, and those of non-topologically massive gravity origin, Bianchi types VI{sub 0} and VII{sub 0}. For a special relation between the cosmological and mass parameters, {lambda}=m{sup 2}, they also include conformally flat solutions, and, in particular, those being locally isometric to the previously-known Kaluza-Klein type AdS{sub 2}xS{sup 1} or dS{sub 2}xS{sup 1} solutions. For nonconstant scalar curvature, all the solutions are conformally flat and exist only for {lambda}=m{sup 2}. We find two general metrics which possess at least one Killing vector and comprise all such solutions. We also discuss some properties of these solutions, delineating among them black hole type solutions.},
doi = {10.1103/PHYSREVD.83.084032},
url = {https://www.osti.gov/biblio/21541498}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 8,
volume = 83,
place = {United States},
year = {2011},
month = {4}
}